Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition
Abstract
We show that the peak which can be observed in fidelity susceptibility around the Berezinskii-Kosterlitz-Thouless transition is shifted from the quantum critical point (QCP) at Jc to J* in the gapped phase by a value |J*–Jc| = B2/36, where B2 is a transition width controlling the asymptotic form of the correlation length ξ~exp(–B/√|J–Jc|) in that phase. This is in contrast to the conventional continuous QCP where the maximum is an indicator of the position of the critical point. The shape of the peak is universal, emphasizing the close connection between fidelity susceptibility and the correlation length. Here, we support those arguments with numerical matrix product state simulations of the one-dimensional Bose-Hubbard model in the thermodynamic limit, where the broad peak is located at J* = 0.212 that is significantly different from Jc = 0.3048(3). In the spin-3/2 XXZ model the shift from Jc = 1 to J* = 1.0021 is small but the narrow universal peak is much more pronounced over the nonuniversal background.
- Authors:
-
[1];
[1]
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Jagiellonian Univ., Krakow (Poland)
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1572334
- Alternate Identifier(s):
- OSTI ID: 1558143
- Report Number(s):
- LA-UR-19-25340
Journal ID: ISSN 2469-9950; PRBMDO; TRN: US2100056
- Grant/Contract Number:
- 89233218CNA000001
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 8; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING; Mathematics; Material Science
Citation Formats
Cincio, Lukasz, Rams, Marek Maria, Dziarmaga, Jacek Piotr, and Zurek, Wojciech Hubert. Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition. United States: N. p., 2019.
Web. doi:10.1103/PhysRevB.100.081108.
Cincio, Lukasz, Rams, Marek Maria, Dziarmaga, Jacek Piotr, & Zurek, Wojciech Hubert. Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition. United States. https://doi.org/10.1103/PhysRevB.100.081108
Cincio, Lukasz, Rams, Marek Maria, Dziarmaga, Jacek Piotr, and Zurek, Wojciech Hubert. Mon .
"Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition". United States. https://doi.org/10.1103/PhysRevB.100.081108. https://www.osti.gov/servlets/purl/1572334.
@article{osti_1572334,
title = {Universal shift of the fidelity susceptibility peak away from the critical point of the Berezinskii-Kosterlitz-Thouless quantum phase transition},
author = {Cincio, Lukasz and Rams, Marek Maria and Dziarmaga, Jacek Piotr and Zurek, Wojciech Hubert},
abstractNote = {We show that the peak which can be observed in fidelity susceptibility around the Berezinskii-Kosterlitz-Thouless transition is shifted from the quantum critical point (QCP) at Jc to J* in the gapped phase by a value |J*–Jc| = B2/36, where B2 is a transition width controlling the asymptotic form of the correlation length ξ~exp(–B/√|J–Jc|) in that phase. This is in contrast to the conventional continuous QCP where the maximum is an indicator of the position of the critical point. The shape of the peak is universal, emphasizing the close connection between fidelity susceptibility and the correlation length. Here, we support those arguments with numerical matrix product state simulations of the one-dimensional Bose-Hubbard model in the thermodynamic limit, where the broad peak is located at J* = 0.212 that is significantly different from Jc = 0.3048(3). In the spin-3/2 XXZ model the shift from Jc = 1 to J* = 1.0021 is small but the narrow universal peak is much more pronounced over the nonuniversal background.},
doi = {10.1103/PhysRevB.100.081108},
journal = {Physical Review B},
number = 8,
volume = 100,
place = {United States},
year = {Mon Aug 19 00:00:00 EDT 2019},
month = {Mon Aug 19 00:00:00 EDT 2019}
}
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Works referenced in this record:
Tensor network states and ground-state fidelity for quantum spin ladders
journal, August 2012
- Li, Sheng-Hao; Shi, Qian-Qian; Su, Yao-Heng
- Physical Review B, Vol. 86, Issue 6
Fidelity Susceptibility Made Simple: A Unified Quantum Monte Carlo Approach
journal, July 2015
- Wang, Lei; Liu, Ye-Hua; Imriška, Jakub
- Physical Review X, Vol. 5, Issue 3
The density-matrix renormalization group in the age of matrix product states
journal, January 2011
- Schollwöck, Ulrich
- Annals of Physics, Vol. 326, Issue 1
At the Limits of Criticality-Based Quantum Metrology: Apparent Super-Heisenberg Scaling Revisited
journal, April 2018
- Rams, Marek M.; Sierant, Piotr; Dutta, Omyoti
- Physical Review X, Vol. 8, Issue 2
Classifying and measuring geometry of a quantum ground state manifold
journal, August 2013
- Kolodrubetz, Michael; Gritsev, Vladimir; Polkovnikov, Anatoli
- Physical Review B, Vol. 88, Issue 6
Universal Work Fluctuations During Shortcuts to Adiabaticity by Counterdiabatic Driving
journal, March 2017
- Funo, Ken; Zhang, Jing-Ning; Chatou, Cyril
- Physical Review Letters, Vol. 118, Issue 10
Precise Extrapolation of the Correlation Function Asymptotics in Uniform Tensor Network States with Application to the Bose-Hubbard and XXZ Models
journal, November 2018
- Rams, Marek M.; Czarnik, Piotr; Cincio, Lukasz
- Physical Review X, Vol. 8, Issue 4
Geometry and non-adiabatic response in quantum and classical systems
journal, June 2017
- Kolodrubetz, Michael; Sels, Dries; Mehta, Pankaj
- Physics Reports, Vol. 697
Fidelity susceptibility of the quantum Ising model in a transverse field: The exact solution
journal, May 2013
- Damski, Bogdan
- Physical Review E, Vol. 87, Issue 5
Optimal quantum estimation in spin systems at criticality
journal, October 2008
- Invernizzi, Carmen; Korbman, Michael; Campos Venuti, Lorenzo
- Physical Review A, Vol. 78, Issue 4
Quantum-enhanced measurements without entanglement
journal, September 2018
- Braun, Daniel; Adesso, Gerardo; Benatti, Fabio
- Reviews of Modern Physics, Vol. 90, Issue 3
Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
journal, March 2008
- Chen, Shu; Wang, Li; Hao, Yajiang
- Physical Review A, Vol. 77, Issue 3
Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit
journal, January 2012
- Mukherjee, Victor; Dutta, Amit; Sen, Diptiman
- Physical Review B, Vol. 85, Issue 2
Numerical studies of ground-state fidelity of the Bose-Hubbard model
journal, March 2014
- Łącki, Mateusz; Damski, Bogdan; Zakrzewski, Jakub
- Physical Review A, Vol. 89, Issue 3
Critical behaviour of spin-s Heisenberg antiferromagnetic chains: analytic and numerical results
journal, March 1989
- Affleck, I.; Gepner, D.; Schulz, H. J.
- Journal of Physics A: Mathematical and General, Vol. 22, Issue 5
Fidelity Approach to Quantum Phase Transitions
journal, September 2010
- Gu, Shi-Jian
- International Journal of Modern Physics B, Vol. 24, Issue 23
Fidelity susceptibility and long-range correlation in the Kitaev honeycomb model
journal, July 2008
- Yang, Shuo; Gu, Shi-Jian; Sun, Chang-Pu
- Physical Review A, Vol. 78, Issue 1
Tensor network decompositions in the presence of a global symmetry
journal, November 2010
- Singh, Sukhwinder; Pfeifer, Robert N. C.; Vidal, Guifré
- Physical Review A, Vol. 82, Issue 5
A practical introduction to tensor networks: Matrix product states and projected entangled pair states
journal, October 2014
- Orús, Román
- Annals of Physics, Vol. 349
Ground-state fidelity in one-dimensional gapless models
journal, November 2007
- Yang, Min-Fong
- Physical Review B, Vol. 76, Issue 18
Critical theory of quantum spin chains
journal, October 1987
- Affleck, Ian; Haldane, F. D. M.
- Physical Review B, Vol. 36, Issue 10
Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid-to-Mott-insulator transition in the one-dimensional Bose-Hubbard model
journal, April 2013
- Carrasquilla, Juan; Manmana, Salvatore R.; Rigol, Marcos
- Physical Review A, Vol. 87, Issue 4
SU magnetism in chains of ultracold alkaline-earth-metal atoms: Mott transitions and quantum correlations
journal, October 2011
- Manmana, Salvatore R.; Hazzard, Kaden R. A.; Chen, Gang
- Physical Review A, Vol. 84, Issue 4
Ground state overlap and quantum phase transitions
journal, September 2006
- Zanardi, Paolo; Paunković, Nikola
- Physical Review E, Vol. 74, Issue 3
Critical dynamics of decoherence
journal, June 2011
- Damski, Bogdan; Quan, H. T.; Zurek, Wojciech H.
- Physical Review A, Vol. 83, Issue 6
Tensor network states and algorithms in the presence of a global U(1) symmetry
journal, March 2011
- Singh, Sukhwinder; Pfeifer, Robert N. C.; Vidal, Guifre
- Physical Review B, Vol. 83, Issue 11
Quantum critical scaling of fidelity susceptibility
journal, February 2010
- Albuquerque, A. Fabricio; Alet, Fabien; Sire, Clément
- Physical Review B, Vol. 81, Issue 6
Quench dynamics near a quantum critical point
journal, January 2010
- De Grandi, C.; Gritsev, V.; Polkovnikov, A.
- Physical Review B, Vol. 81, Issue 1
Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions
journal, January 2015
- Sun, G.; Kolezhuk, A. K.; Vekua, T.
- Physical Review B, Vol. 91, Issue 1
Phase diagrams and correlation exponents for quantum spin chains of arbitrary spin quantum number
journal, November 1986
- Schulz, H. J.
- Physical Review B, Vol. 34, Issue 9
Quantum Monte Carlo Simulations of Fidelity at Magnetic Quantum Phase Transitions
journal, October 2009
- Schwandt, David; Alet, Fabien; Capponi, Sylvain
- Physical Review Letters, Vol. 103, Issue 17
Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
journal, March 2008
- Verstraete, F.; Murg, V.; Cirac, J. I.
- Advances in Physics, Vol. 57, Issue 2
Quantum Fidelity in the Thermodynamic Limit
journal, February 2011
- Rams, Marek M.; Damski, Bogdan
- Physical Review Letters, Vol. 106, Issue 5
Ground-State Fidelity and Bipartite Entanglement in the Bose-Hubbard Model
journal, March 2007
- Buonsante, P.; Vezzani, A.
- Physical Review Letters, Vol. 98, Issue 11
Fidelity approach to quantum phase transitions: finite-size scaling for the quantum Ising model in a transverse field
journal, October 2008
- Zhou, Huan-Qiang; Zhao, Jian-Hui; Li, Bo
- Journal of Physics A: Mathematical and Theoretical, Vol. 41, Issue 49
Quantum Critical Scaling of the Geometric Tensors
journal, August 2007
- Campos Venuti, Lorenzo; Zanardi, Paolo
- Physical Review Letters, Vol. 99, Issue 9
Fidelity susceptibility, scaling, and universality in quantum critical phenomena
journal, June 2008
- Gu, Shi-Jian; Kwok, Ho-Man; Ning, Wen-Qiang
- Physical Review B, Vol. 77, Issue 24
Quantum critical scaling of fidelity in BCS-like model
journal, July 2013
- Adamski, Mariusz; Jȩdrzejewski, Janusz; Krokhmalskii, Taras
- Journal of Statistical Mechanics: Theory and Experiment, Vol. 2013, Issue 07
Ultracold bosons with short-range interaction in regular optical lattices
journal, January 2016
- Krutitsky, Konstantin V.
- Physics Reports, Vol. 607
Fidelity, dynamic structure factor, and susceptibility in critical phenomena
journal, August 2007
- You, Wen-Long; Li, Ying-Wai; Gu, Shi-Jian
- Physical Review E, Vol. 76, Issue 2
Quench dynamics near a quantum critical point: Application to the sine-Gordon model
journal, June 2010
- De Grandi, C.; Gritsev, V.; Polkovnikov, A.
- Physical Review B, Vol. 81, Issue 22
Scaling of ground-state fidelity in the thermodynamic limit: model and beyond
journal, September 2011
- Rams, Marek M.; Damski, Bogdan
- Physical Review A, Vol. 84, Issue 3
Exact results for fidelity susceptibility of the quantum Ising model: the interplay between parity, system size, and magnetic field
journal, December 2013
- Damski, Bogdan; Rams, Marek M.
- Journal of Physics A: Mathematical and Theoretical, Vol. 47, Issue 2
Works referencing / citing this record:
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